标题： 关于$ζ$与卡西米尔能量截止正则化的联系 显示英文标题

标题： Connection between $ζ$ and cutoff regularizations of Casimir energies

摘要： 我们研究了标量场的$\zeta $正则化和截止正则化的卡西米尔能量之间的联系。我们表明，一般来说，这两种正则化方案都会导致发散项，并且有限部分也不一致。我们确定了一种方法中出现的各种系数与另一种方法中的关系。作为应用，我们讨论了在周期性边界条件下$d$维盒子中标量场的情况。 显示英文摘要

摘要： We study the connection between $\zeta $- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to finite parts which do not coincide. We determine the relationships among the various coefficients appearing in one approach and the other. As an application, we discuss the case of scalar fields in $d$-dimensional boxes under periodic boundary conditions.